\documentclass{article} \usepackage{german} \setlength{\textwidth}{135mm} \begin{document} \noindent Aus der \emph{l'Hospitalschen} Regel folgt: \[ \lim_{x\to0}\frac{\ln\sin\pi x}{\ln\sin x} = \lim_{x\to0}\frac{\pi\frac{\cos\pi x}{\sin\pi x}}{\frac{\cos x}{\sin x}} = \lim_{x\to0}\frac{\pi\tan x}{\tan\pi x} = \lim_{x\to0}\frac{\pi/\cos^2 x}{\pi/\cos^2 \pi x} = \lim_{x\to0}\frac{\cos^2\pi x}{\cos^2 x} = 1 \] \end{document}